Throughout this description, various publications are cited as representative of related art. For the sake of simplicity, these documents will be referred by reference numbers enclosed in square brackets, e.g., [x]. A complete list of these publications, ordered according to the reference numbers, is reproduced in the section entitled “List of references” at the end of the description. These publications are incorporated herein by reference.
In digital transmission systems, one technique to transmit source bits is to group them into complex symbols representing the amplitude and phase of the signal modulating a frequency carrier. Quadrature Amplitude Modulation (QAM) and Phase Shift Keying (PSK) are exemplary modulation schemes.
Generally, the QAM (or PSK) complex symbols are associated with m binary bits, and the way the bits are associated to the S=2m complex symbols is called “mapping”, while the set of symbols is called a “constellation”.
For example, Quadrature Phase Shift Keying (QPSK) refers to four complex symbols that can be represented by the two bits 00, 01, 10, 11 respectively. In this context, Gray mapping is a well-known exemplary technique wherein two adjacent complex symbols represent group of bits differing by only one bit.
Complex symbols can be graphically represented in the complex plane where the two axes represent the in-phase (I) and quadrature-phase (Q) components of the complex symbol. For example, FIG. 1 illustrates an example QPSK constellation, wherein the four constellation symbols are denoted 00 to 03. The corresponding Gray-mapped pairs of bits are indicated in blocks 04 to 07. A possible received symbol 08 is also shown, which does not coincide with any transmit symbol due to the effect of noise and distortion caused by the channel.
Digital data (bits or symbols) are transmitted through physical channels that normally corrupt them because of additive noise. Moreover, in wireless systems, the fading communication channel imposes distortion (i.e., phase and amplitude changes). For these reasons, the received data typically do not coincide with the transmitted ones, and a technique, such as an equalization technique, is required to estimate the transmitted data. Normally, the channel coefficients are estimated prior to such equalization and assumed known by the equalizer. The robustness of a transmission link depends on the ability of the receiver to reliably detect the transmitted bits (i.e., transmitted 1s as 1s and transmitted 0s as 0s).
Signal reflections and diffractions can result in multiple copies of the transmitted signal at the receiver, i.e., multi-path effects. Typically, each of these multi-path components will be characterized by a different phase and magnitude associated with the channel.
For example, the discrete time-domain Channel Impulse Response (CIR), and its associated Power Delay Profile (PDP), represents each multi-path contribution as a time-domain tap. Each tap is typically represented as a complex value whose magnitude represents the associated level of intensity, and the angle a phase rotation, of its contribution to the overall received signal. Moreover, the delay spread of the channel is the delay between the arrival of the first and last multi-path contributions in the PDP. Often used is a single value, which accounts for each multi-path contribution, a root-mean square (rms) delay spread, which measures the delay dispersion around its mean value. The signal will likely be distorted by channels characterized by a higher rms delay spread.
Moreover, in the digital domain, an alternative practical parameter to characterize the channel in the time domain is the channel length (CL), i.e., the number of relevant channel taps.
Time-domain multi-path effects may have a dual representation in the frequency domain, where they determine the level of “frequency selectivity” of the channel, measured through the coherence bandwidth, inversely proportional to the delay spread, which represents a frequency band where the channel frequency-response amplitude assumes almost a constant value.
A popular wireless modulation technique is represented by orthogonal frequency division multiplexing (OFDM). OFDM systems correspond to dividing the overall information stream to be transmitted into many lower-data-rate streams, each one modulating a different “sub-carrier” of the main frequency carrier. Equivalently, the overall bandwidth is divided into many sub-bands respectively centered on the sub-carriers. This operation makes data communication more robust via a wireless multi-path fading channel, and simplifies frequency equalization operations. OFDM systems are well known to those skilled in the art. Examples of popular OFDM-based wireless communication systems include, though not limited to, the Wireless Local Area Network (WLAN) standardized by IEEE as “802.11a” [1] and others like “WiMax” for fixed wireless access, “LTE” (long-term evolution) for next-generation cellular communications, etc.
State-of-the-art channel-estimation (CE) methods for OFDM systems may be classified in several ways, such as (see [2], [3]):                Frequency or Time Domain: Channel-estimation techniques in the frequency domain (FD) are usually simpler, since they can be applied to small groups of subcarriers, or independently subcarrier by subcarrier; on the other hand, time domain (TD) CE typically aims to minimize the mean-square error by a proper weighting of the channel impulse response (CIR), on the basis of some additional information, such as the delay spread or the PDP values. FD CEs are usually performed by a Zero Forcing (ZF) technique applied to each tone, while TD CEs may be based on a Maximum Likelihood (ML) criterion.        Pilot or Data Aided: “Pilots” denote training symbols, known at both the transmitter and receiver sides and usually inserted into the preamble or within the data payload at some subcarrier indexes for the purpose of synchronization or CE [2]. For what concern CE, training symbols are usually placed into Long Training Fields (LTFs) and this scheme will be referred as Pilot-Assisted Channel Estimation (PACE). As an example, systems [1] use two OFDM modulated LTFs (denoted in this document as LTF1 and LTF2). The class of Data-Aided CE algorithms exploits decoded data symbols as if they were known pilots, in order to refine previous channel estimates and track channel variations (induced for example by Doppler effect). These schemes will be referred as Data-Aided Channel Estimation (DACE) algorithms.        